Much of the eastern part of Brittany has a regional language, but it’s not Breton. Gallo is not a Celtic language like its neighbour, but is part of the same Romance group of languages (ie those descended from Latin) as French. Because of their similarity, Gallo is often wrongly assumed to be a patois or dialect of French; it’s actually a separate language in its own right.
However, it has suffered the same suppression as Breton, a long process which began in 1539 when the Villers-Cotterêts Decree made French alone the official language of the country. Although the purpose of that law was to end the use of Latin, its side-effect was to downgrade France's other languages. By the seventeenth century, regional languages were relegated by the state to the status of patois. In the twentieth century, compulsory education was in French and aimed to dissuade children from speaking other languages.
The state’s attempt to eradicate languages such as Gallo and Breton involved discouraging a huge proportion of the country from speaking their mother tongues: French was the language of the regions around Paris, while most of the rest of the country spoke a range of regional languages. However, as speaking French became a mark of education and modernity, other languages were often simply not passed on from parent to child. The numbers of Gallo and Breton speakers declined sharply from the 1950s.
Nobody knows for sure how many people still speak Gallo, since the language is not officially recognised (France still has not raftified the European Charter for Regional or Minority Languages). Even in the region it has a much lower profile than Breton, despite being the language of its capitals Rennes and Nantes. Although it tends to be perceived as a dying language spoken by older people, younger people are learning it and it is taught in many local schools. Poets, novelists and cartoonists are writing in Gallo, which also has a strong oral and musical tradition, and there is an annual festival. You can learn it here; there’s lots of information in languages including English here.